Question

What is the solution to the equation x8 − 5 = −3
solving for x
?(1 point)

−64

1

−16

16

Answer 1

To solve the equation \( x^8 - 5 = -3 \), we first add 5 to both sides:

\[
x^8 - 5 + 5 = -3 + 5
\]

This simplifies to:

\[
x^8 = 2
\]

Next, to solve for \( x \), we take the eighth root of both sides:

\[
x = \pm 2^{1/8}
\]

Since \( 2^{1/8} \) is a positive value, we only need to find the numerical approximate. However, none of the provided answer choices (-64, 1, -16, 16) are equivalent to \( 2^{1/8} \) or \( -2^{1/8} \).

Let’s analyze what these answers represent as potential values for \( x \):

1. \( -64 \): \( (-64)^8 \neq 2 \)
2. \( 1 \): \( (1)^8 = 1 \) (not a solution)
3. \( -16 \): \( (-16)^8 \neq 2 \)
4. \( 16 \): \( (16)^8 \neq 2 \)

Therefore, none of these choices are correct solutions based on the calculation.

Given the context of your question, if we need to evaluate numerically:

The closest numerical approximation of \( 2^{1/8} \) is about \( 1.0905 \). Since this value is not directly given in the choices, and since \( 1 \) is the closest provided option, one might consider choosing \( 1 \) for the purposes of a multiple choice activity, although strictly speaking it is not a correct solution.

So, the answer is:

**1 (approximately)**, though it’s important to note it is not an exact solution to \( x^8 = 2 \).